The Manchester City goalkeeper dislocated his left shoulder and also suffered tendon and ligament damage when saving Abou Diaby's shot during the goalless draw at Arsenal in late April.
The setback saw City bring in Sunderland's Marton Fulop as cover on an emergency loan basis, but 34-year-old Given expects to be ready to reclaim his place in August after a summer of conditioning work.
"I saw the specialist on Thursday and he was pleased with my progress. He said if anything I'm ahead of schedule so that's good news," he told Sky Sports News.
"I've been training all week in Manchester with the physios. It'll be a different summer for me but the most important thing for me is to get back for the new season and that's my target.
"That's the plan and after yesterday's meeting I should be okay."
Given kept 13 clean sheets and conceded 52 goals in his 44 appearances for City last season.